Home > Publications > Abstract

Marginal Analysis of Point Processes with Competing Risks

Cook, R. J., Chen, B. E. and Major, P.

Handbook of Statistics, Vol. 23.

Point process data arise in medical research when a clinically important event may recur over a period of observation. Examples are ubiquitous and arise in settings such as oncology (Gail et al., 1980; Byar et al., 1986; Hortobagyi et al., 1996), cerebrovascular disease (Hobson et aL, 1993; OASIS, 1997), osteoporosis (Riggs et al., 1990), and epilepsy (Albert, 1991). Interest typically lies in understanding features of the event process such as intensity, rate, or mean functions, as well as related group differences and covariate effects. The method of analysis for point process data is naturally driven by the feature of interest. Andersen etal. (1993) focus on intensity-based methods for counting processes, while others emphasize models with a random effect formulation (Thall, 1988; Abu-Libdeh et al., 1990; Thall and Vail, 1990), marginal methods for multivariate survival data (Wei et al., 1989), or marginal models based on rate functions (Lawless and Nadeau, 1995). Interpretation and fit are key factors which help guide the analysis approach for a given problem, and the merits of the various strategies have been actively discussed in the literature (Lawless, 1995; Wei and Glidden, 1997; Cook and Lawless, 1997 a; Oakes, 1997; Therneau and Hamilton, 1997; Cook and Lawless, 2002). Often marginal rate functions serve as a meaningful basis for inference and these will serve as the focus here.

Frequently when subjects are at risk for recurrent events, they are also at risk for a so-called terminal event which precludes the occurrence of subsequent eVi;mts. Death, for example, is a terminal event for any point process generated by a chronic health condition. The presence of a terminal event with point process data raises challenges which must be addressed if interest lies in the mean function (Cook and Lawless, I 997b ), the cumulative distribution function for the number of events over a fixed interval or a lifetime (Strawderman, 2000), or other aspects of the process. The purpose of this article is to describe methods of analysis for point process data in the presence of terminal events while emphasizing connections with methodology for the competing risks problem in survival data.


free hit counters